Coarse registration of point clouds with low overlap rate on feature regions

Abstract

In order to solve the problems of long time consuming and easy failure of the existing coarse registration algorithms based on global registration on two 3D point clouds with low overlap rate, we proposed a coarse registration algorithm based on feature regions and the Super 4-Points Congruent Sets (SUPER4PCS) algorithm. Firstly, intrinsic shape signatures (ISS) algorithm was used to extract and describe the features of the down-sampled point clouds. Secondly, the feature point clouds were divided into regions and the initial overlapped sub-regions were extracted. Thirdly, the complete overlapping regions were grown from the overlapped sub-regions and gradually recovered. Finally, the SUPER4PCS was used for registration on the complete overlapping regions. The experimental results showed that the geometric accuracy, registration success rate, and robustness of the proposed algorithm were better than that of SUPER4PCS and its improved algorithms, and the time consumption was one order of magnitude lower than that of SUPER4PCS on point clouds with low overlap rate.

Introduction

With the maturity of 3D data acquisition technology, 3D point cloud registration has been applied in more scenes. Point cloud registration refers to transforming the point cloud data of the same model from different perspectives into a common coordinate system and stitching them together [1]. It is a crucial step in the 3D reconstruction of scene [2], object recognition [3], augmented reality [4], robot positioning and navigation and automatic map building [5], [6], etc. The efficiency and accuracy of registration have a very important influence on the whole project.

There are many solutions for point cloud registration, and most of the existing registration methods can be divided into coarse registration and fine registration [7], both of which aim to obtain the rigid transformation between source and target clouds. Coarse registration quickly estimates the rigid motion between two corresponding clouds to provides a good initial value for fine registration, so as to both reduce the computational burden and avoid the problem that the direct fine registration may fall into local optimization. On the basis of coarse registration, fine registration is carried out by means of iterative closest point (ICP) or least square surface matching. All the optimal fine registration methods have one thing in common: they locally minimize the non-convex error function and therefore require an initial alignment that is accurate enough to converge to a desired solution [8], [9]. The global registration algorithm and a series of improved algorithms [10], [11], [12], [13] represented by the classic ICP algorithm [14], [15] have higher registration accuracy, but these methods require good initial values of two point clouds to avoid falling into the local optimal solution, which will lead to the failure of registration. At the same time, [16], [17] point out that coarse registration is more difficult and important than fine registration. Therefore, the key step of point cloud registration is coarse registration.

Common coarse registration methods are divided into the hypothesis and test method represented by RANSAC and the method represented by 4PCS based on geometric shape characteristics. Rigid-body transformation can be solved according to three corresponding point pairs [18]. Therefore, point cloud registration can be regarded as a search problem. Assuming that the input point cloud P and Q contain m and n points respectively, the simplest exhaustive search method is to select three point pairs from P and Q each time, through which the rigid body transformation and registration error are calculated, and the rigid body transformation with the minimum error is selected as the optimal transformation. Obviously, the time complexity of exhausting search is O(${\mathit{m}}^3$ ${\mathit{n}}^3$). Fischler et al. [19] proposed the RANSAC algorithm, which collects two points randomly in two clouds of point sets and uses the Euclidean distance and normal vector between points to determine the corresponding relationship of points. Two groups of points with normal vectors can determine a rigid body transformation. However, the algorithm is instable and easy to produce wrong correspondence. Irani et al. [20] further reduced the search complexity to O(${\mathit{mn}}^3$logn) based on the RANSAC, but it is still not applicable to large-scale point cloud.

In order to reduce the three-power search complexity of RANSAC and other algorithms, Aiger et al. [21] proposed the 4-points congruent sets (4PCS) algorithm, which reduces the search complexity to O(${\mathit{n}}^2$). Using the properties of rigid body transformation, the 4PCS algorithm randomly selects four coplanar points on P as a set of bases, searches for all the coplanar 4-points sets of approximately congruent points on Q and registers them, and selects the transformation with the minimum registration error as the final solution. However, 4PCS has two steps to be improved: (1) In the process of searching the congruent sets, for the given base B in P, the time complexity of finding two pairs of given distances ${\mathit{r}}_1$ and ${\mathit{r}}_2$ from Q is quadratic. (2) In the bases matching process, a large number of redundant candidate 4-points pairs lead to a waste of time. In view of the two problems existing the 4PCS, some researchers have proposed improvements to the 4PCS method. Theiler et al. [8], [16] proposed Keypoint-based 4-points congruent sets (K-4PCS) algorithm. The algorithm firstly extracts the key points from the original point clouds, and then uses the key point set instead of the original point cloud to match the clouds, which reduces the size of the searched point set. Silva et al. [22] pointed out that 4PCS algorithm requires manual estimation of overlap rate and put forward the dynamic 4-points congruent sets (D4PCS) algorithm. The algorithm automatically estimates the overlap rate of two point clouds in each iteration to estimate the optimal length of the base, which improves registration accuracy, calculation speed and robustness to some extends. However, the algorithm needs a large enough overlap ratio of two point clouds. Another type of effective method is to improve the structure of the base. Mohamad et al. [23] introduced a more general 4-points model (Generalized 4PCS) with the concept of distance between point pairs, which reduces the number of candidate bases and thus improves the efficiency of the algorithm. Huang et al. [24] proposed the Volumetric 4PCS algorithm that adds the concept of volume consistency when constructing the coplanar 4-points base, which extends the coplanar 4-points matching to non-coplanar 4-points matching and improves the operational efficiency of the algorithm. Xu et al. [25] proposed the MSSF-4PCS algorithm, which adds normal vector constraint to reduce the number of 4-points pairs, and further optimizes the matching results by extracting and matching feature points in the neighborhood with radius R of 4-points pair, so as to improve the accuracy and operation speed of registration. Due to the complexity of the quadratic still greatly limits the applicability of these registration algorithms in the large point cloud, Mellado [17] put forward Super 4-points congruent sets (SUPER4PCS) algorithm, which realizes the fast extraction of point pairs and reduces the complexity to O(n) by rasterizing the target point cloud and increasing the angle constraint of the 4-points base. On this basis, Mohamad et al. [26] proposed Super Generalized 4PCS, which generalizes the construction of coplanar 4-points basis and no longer strictly restricts the 4-points coexisting in a plane, thus further improving the efficiency of point cloud registration.

4PCS and its improved algorithms have improved the registration efficiency to some extent, but for low overlap point cloud, these algorithms still have problems of insufficient efficiency and falling into local optimum. This is because: (1) These algorithms register the entire point cloud directly and extract the basis from all points, which results in most of the search time being wasted in non-overlapping regions. (2) The global largest common point set (LCP) is used to measure the registration accuracy, which leads to the result that the overlap rate of the two point clouds is required to be large enough.

Thus, it can be seen that the coarse registration problem with low overlap rate point cloud deserves our attention. The main problems of coarse registration are as follows: (1) How to extract effective rotation invariant features? Because point clouds are partially overlapping, global geometric invariants such as centroid and Principal Component Analysis (PCA) cannot be directly used. (2) How to quickly find the overlapping region? Because the rigid body transformation is a low dimensional linear transformation and a few accurately matched point pairs can be better described than most mismatched point pairs. In order to avoid the waste of search time in non-overlapping regions with more mismatches, registration should be performed only in overlapping regions. In conclusion, the coarse registration method of low overlap point cloud is of great research significance.

Aiming at these problems, Raposo et al. [27] proposed 2PNS algorithm, which is an improvement of SUPER4PCS. The algorithm only uses the topological relationship between two points and normal vector to construct the matching rules. In the scene without point noise, the algorithm speeds up by two orders of magnitude, and 5.2 times in Kinect scanning data. At the same time, it can cope with the scene registration with a minimum overlap rate of 5%. In addition, some scholars proposed registration methods at the regional level. Han et al. [28] proposed taking regions as basic registration objects, thus the global registration could be transformed into regional registration through regional division and regional registration, which can effectively deal with 3D point clouds with low overlap rate, but there is a big computational problem. Wang et al. [29] divided the original point clouds into regions through spectral clustering and then achieved registration through the shape descriptor between regions. Liu et al. [30] extracted the overlapping region boundary of the original point clouds and used the boundary features to assist the selection of bases to improve the efficiency of the 4PCS algorithm. However, there are some problems of long running time and the need of prior information of overlap rate and. Gan et al. [31] proposed a region segmentation method based on normal difference and curvature difference, which has the problem of large amount of calculation when computing the normal vector and curvature on the original complete point clouds. Compared with global registration algorithms such as 4PCS, recent methods focus on the extraction of overlapping regions, which improves the success rate and search speed of registration with low overlap rate to some extent. However, the efficiency and stability of the algorithms still need to be improved.

Considering the limitations of the existing methods, our goal is to establish a stable and fast coarse registration algorithm on point clouds with low overlap rate, which can improve the success rate and accuracy compared with the existing state-of-the-art global registration methods, so as to provide a better initial value for fine registration. Our core idea is to focus on the extraction and registration of overlapping regions. Therefore, we propose a coarse registration algorithm for point clouds with low overlap rate on feature regions. The main contributions of this paper are:

• We propose a novel coarse registration algorithm which does not require the prior information of overlap rate. The algorithm transforms the complex large-scale global registration problem into simple small-scale overlapping regions registration problem by extracting overlapping regions and registering only on them. It is confirmed by quantitative and qualitative evaluations that the proposed algorithm has higher accuracy, success rate, robustness and lower time consuming than the existing coarse registration algorithms on point clouds with low overlap rate.

• We are the first to propose an efficient and complete algorithm framework which force on extracting overlapping regions to solve the problem of registration on point clouds with low overlap. The proposed algorithm framework is flexible and extensible, and it can be combined with more advanced feature extraction and region division methods in the future.

• We have evaluated the proposed algorithm in detail, and the results show that our method can work well on both synthetic and real-scenes datasets.

This paper is arranged as follows. Section 2 briefly reviews the 4PCS and SUPER4PCS algorithms. Section 3 introduces the proposed algorithm. Section 4 shows the quantitative and qualitative evaluation results on synthetic and real-scenes datasets. Section 5 summarizes the works, points out the existing problems, and introduces the future works.